blood comes from bone marrow
This is actually quite common. The blood you see comes from the bone marrow. Cooking forces it out of the marrow and through the porous bones into the meat. As long as your chicken is cooked to a safe temperature, it's safe to eat.
safe to eat
If the chicken is cooked to a food-safe internal temperature in the normal amount of time and the blood comes from the bone marrow, your chicken is safe to eat.
Check the chicken breast
Since the leg meat is close to bone filled with marrow, it is difficult to judge visually. If you're too worried, use a thermometer. If you are cooking a whole chicken I recommend checking the breast as it will be white when cooked so it is easier to tell and if the breast is cooked you can be sure the rest is cooked.
Chicken breasts cook much faster than legs and thighs, which is why you always measure the temperature in a few places or through the internal temperature deep in the thigh as it is the last to finish cooking and reach a safe temperature place.
It is important to ensure that the chicken is cooked correctly and at a safe temperature. This is because some microorganisms are often found on chicken that can make you sick. Cooking chicken until its internal temperature reaches 165°F (74°C) kills these microorganisms.
Thoroughly cooked chicken blood
If you eat thoroughly cooked chicken blood, nothing particularly dangerous will happen. Unless the chicken is chemically poisoned (as opposed to microbially poisoned), such as being filled with hormones. But even in this case, a one-time event, a small amount of blood taken with food, would not cause any harm.